After staying quiet following Arizona’s passage of a controversial new immigration law, a number of national Republican voices have begun to criticize it as heavy-handed.

While none of the GOP critics who are speaking out go as far as liberal critics who have called the bill “racist,” they do believe the bill is not the correct approach and hope it prompts the federal government to step in.

Florida Senate candidate Marco Rubio said in a statement Tuesday that he fears the law puts the Arizona’s police force in an “incredibly difficult position.”

“It could also unreasonably single out people who are here legally, including many American citizens,” Rubio said. “Throughout American history and throughout this administration we have seen that when government is given an inch it takes a mile.”

Rubio criticism was quickly followed up by a fellow Floridian, former Gov. Jeb Bush. In an interview with POLITICO, Bush said the law is not “the proper approach.”

“I think it creates unintended consequences,” he said. “It's difficult for me to imagine how you're going to enforce this law. It places a significant burden on local law enforcement and you have civil liberties issues that are significant as well.”

Much of the criticism is coming from associates of former President George W. Bush.

“I wished they hadn’t passed it,” Bush strategist Karl Rove told a crowd of 500 at a senior community center in Florida. “I think there is going to be some constitutional problems with the bill….At the end of the day,” he said, “I think there are better tools.”

Conservative Washington Post columnist Michael Gerson, a former Bush speechwriter, called the law “dreadful” on Wednesday in his piece for the Post. “This law creates a suspect class, based in part on ethnicity, considered guilty until they prove themselves innocent,” Gerson wrote. “It makes it harder for illegal immigrants to live without scrutiny — but it also makes it harder for some American citizens to live without suspicion and humiliation.”

“Americans are not accustomed to the command ‘Your papers, please,’ however politely delivered,” he continued. “The distinctly American response to such a request would be ‘Go to hell,’ and then ‘See you in court.’”

Former Bush press secretary Dana Perino questioned the law in a post earlier this week in POLITICO’s Arena forum. “I understand that Arizonans are frustrated with the level of illegal immigration,” she wrote, “ and at the same time I can't imagine that we're going to allow police to stop people on the streets and demand their papers. Stronger enforcement is key, but this seems a bridge too far.”

Former Alaska Gov. Sarah Palin defended the bill during an interview Tuesday with Fox News’ Sean Hannity and blamed President Barack Obama for pushing the “myth” that the law allows racial profiling.

But while Palin and many of the party’s social conservatives have voiced support for the law, there is a clear drum beat of Republicans who oppose Arizona’s approach.

On Capitol Hill, only two Republicans so far have spoken out against the law, South Carolina Sen. Lindsey Graham and Florida Rep. Lincoln Diaz-Balart.

Graham, a supporter of Bush’s 2006 immigraiton bill bill, said the law “doesn’t represent the best way forward” while Diaz-Balart “strongly” disagrees with the state’s approach.

“It alters American tradition and long-standing policy making immigration law enforcement a federal matter,” said the Congressman. “And it strikes fear in the hearts of many American citizens and legal residents.”

Several prominent conservative commentators have been less tempered in their criticism of the law.

“It does offend me that when one out of every three citizens in the state of Arizona are Hispanics, and you have now put a target on the back of one of three citizens,” MSNBC host Joe Scarborough said Tuesday during his show “Morning Joe.”

“I will tell you that this is un-American,” said the former Republican congressman. “It is unacceptable, and it’s un-American.”